Considering the effectiveness of my adaptation to prospect theory

My adaptation of PT accounts for the effect surprise has on the evaluations of

future decisions in games with several rounds. The value function I originally proposed is

written below. As a reminder, let Vt represent the value of a given prospect in round t of a

multi-round round game, xi represent the given prospect in round t, pi represent the

probability of xi, xt-1 represent the outcome of round t-1 in the game, ψt-1 represent the

location of the expectations-based reference point along the x-axis of the value function,

and ut-1 represent the value function for the outcome of round t-1.

Vt=∑𝒏𝒊=𝟏𝝅(𝒑𝒊) ∗ 𝒗[𝒙𝒊+ 𝒖𝒕−𝟏(𝒙𝒕−𝟏− ψ𝒕−𝟏 )]

According to this model, negative surprises in time period 1 cause prospects to be

evaluated more negatively in time period 2, and positive surprises in time period 1 cause

prospects to be evaluated more positively in time period 2. Finally, surprises affect

behavior in the second time period more as the surprise grows, and likewise the more one

round. I also hypothesized that surprises outcomes increase the utility one experiences for

both negative and positive outcomes compared to expected outcomes.

Based on my results, there is strong evidence that surprise does increase the utility

of outcomes, but I was unable to find any evidence that surprises are affecting the

evaluation of future prospects differently than expected outcomes. There are still several

variables influencing decision-making behavior that are unaccounted for by the variables

I test in this paper.

Beyond just my experimental results, the theory is only valuable if it can

sufficiently explain behavior in the real world. My findings support Vanhamme and

Snelders’s (2001) conclusion that surprise is associated with increased consumer satisfaction. My theory also provides a reasonable explanation as to why PEAD, strategic

earnings forecasts by firms, and non-linear reactions by investors to expected and

unexpected monetary policy changes occur. Earnings surprises cause the value of a

company to be greater than had that company’s earnings not been a surprise, increasing

demand for their stocks. Warning of long-term structural losses reduces negative investor

reactions to those losses. Unexpected monetary policy changes discourage investors more

than expected monetary policy changes. In each situation, the theory that surprise

outcomes increase the utility magnitude of outcomes can be applied to give a reasonable

explanation for why these behaviors occur. But in none of these situations do the factors

that influence the current decision result solely from the weighting of current prospects

and the outcome of previous time period, as my theory suggests.

As it stands, the adaptation to PT I propose is only functional in two round games.

This may not be the best model for decision-making behavior in real life, because there

affect behavior. Loewenstein and Elster (1992) use an example of seeing a movie to show

that the effects of reference point shift following an event may be long lasting. If I see an

incredibly good movie, 15 years from now I may not remember exactly what happens in

the movie, but my tastes for movies will still be altered. Clearly, taste for movies is not

only affected by how you felt about the one movie you had watched previous to the

current one.

The effect of prior outcomes on future evaluations may be a ratio of the effect of

the previous outcome over the average effects of all previous rounds, keeping in mind

that utility of an outcome increases as surprise increases. A model fitting these

characteristics looks like this:

Vt=∑𝒏_𝒊=𝟏𝝅(𝒑_𝒊) ∗ 𝒗[𝒙_𝒊+ 𝒖_𝒕−𝟏(𝒙_𝒕−𝟏)/ ∑𝒏_𝒕=𝟏𝒖(𝒙_𝒏)]

According to this model, surprise has the largest effect on behavior in early

rounds, or in the round immediately following the surprise. As the game goes on, it takes

either consistently different results or a very large surprise in order to influence

behavior.7

Despite the fact that my findings show surprise increases reference point

adaptation following an outcome, there are intuitive scenarios where this may not be true.

For example, consider a game that has been repeating for a very long time where there is

a safe option A and a risky option B. In each round, my prospects are exactly the same. I

always choose the safe option, and always get the payoff associated with the safe option.

If I choose the safe option and something else happens, my reference point may not shift

as I perceive this surprise as an error rather than new information that needs to be

7 _{This model may explain behavior in games with relatively few rounds well. In truly infinitely repeating}

games, a more complex function which accounts for forgetting some outcomes over time may be even better at explaining behavior.

accounted for. In a game which has just started, a surprise outcome may be seen as new

information that needs to be weighted heavily into the evaluation of prospects. More

research into how surprise affects reference point shift must be done. Moreover,

including reference point shift in the multi-round PT value function may provide a better

model of behavior in multiple rounds.

In summary, my adaptation to PT brings us a step closer to explaining behavior in

games with multiple rounds, but more research and adjustment of the theory must be

done to have a truly comprehensive model of what influences decision-making. The

theory can be applied to explain behaviors we observe to a limited degree, and the data

from my experiments supports the theory’s predictions concerning utility. But the majority of situations in life are not simple two round games as the theory assumes.

Therefore, my adaptation to PT is strongest in terms of explaining behavior in an

experimental setting with two round games. A better model for behavior in games with

multiple rounds will account for the effects that many rounds have on behavior, rates of

forgetting distant outcomes, and varying levels of ex-post reference point shift.